Question

When a mass on a spring is at maximum displacement, what quantity is at a minimum?

Answer 1

The velocity

Step-by-step explanation:

For a mass-spring system, the total mechanical energy is constant during the motion. The total mechanical energy is sum of the elastic potential energy, U, and the kinetic energy, K:

`E=U+K=(1)/(2)kx^2+(1)/(2)mv^2`

where

k is the spring constant

x is the displacement

m is the mass

v is the velocity

Since E must remain constant, we see that when x increases, v decreases, and vice-versa. Therefore, when x (the displacement) is at maximum, v (the velocity) is at minimum (more precisely, it is zero).